Discontinuous coherent wave acoustic holography

ABSTRACT

The response to deep reflecting layers in an acoustic hologram is improved by varying the time at which acoustic wave relating to to various images are radiated either by pulsing the source of coherent waves or turning the source off after a steady state has been established and gating the receivers so that acoustic waves relating to very strong and very weak images are not being received at the same time.

- waited tates Famine Smith, in. June 27, 1972 [s41 DHSCONTINUOUScoimREN'r WAVE [s61 References Cited ACUUSTIC HOLOGRAPHY UNITED STATESPATENTS [721 Imam Bella, 3,461,420 8/1969 Silverman ..340 1 73 Assignee:Shell on Company, New York, NY. 3,474,404 10/1969 Silvefman- "340/1553,484,740 12/1969 Cook ..340/l5.5 [22] Filed: Feb. 3, 1970 PrimaryExaminer-Benjaniin A. Borchelt [21] Appl' 8206 Assistant Examiner-N.Moskowitz Related Us. Application Dam Attorney-Theodore E. Bieber and J.H, McCarthy [63] Continuation-in-part of Ser. No 659,984, Aug. 8,ABSTRACT 7 3,503,037 The response to deep reflecting layers in anacoustic hologram is improved by varying the time at which acoustic waverelat- [52] US. Cl. ..340/l5.5H i to t riou images are radiated eitherby pulsing the [51] Int. Cl. ..G01v 1/34 source of coherent waves orturning the source off after a [58] Field of Search .340/155, 15.5 H;181/.5 steady state has been established and gating the receivers sothat acoustic waves relating to very strong and very weak images are notbeing received at the same time.

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DISCONTINUOUS COHERENT WAVE ACOUSTIC HOLOGRAPI-IY CROSS-REFERENCE TORELATED APPLICATIONS This application is a continuation-in-part of acopending application of N. D. Smith, Jr., Ser. No. 659,984 filed Aug.8, 1967 and entitled Holographic Seismic Exploration, now U.S. Pat. No.3,503,037.

BACKGROUND OF THE INVENTION Reflection seismology for the exploration ofthe sedimentary layers of the earth to great depths (15 to 20,000 feet)depends on the following properties of the rocks:

1. Various geological strata of interest having different acousticimpedances.

2. The variations in the strata are not too great and reflectioncoefiicients are usually 0.01 or less and only in unusual cases reaches0.05 to 0.10.

3. Attenuation is sufficiently low for frequencies below 60 I-Ierz thatsignals above noise can be recorded over path lengths of 40,000 feet.

4. At wave-lengths corresponding to these frequencies the layers areremarkably smooth and hence the layers reflect specularly.

The thickness of layering varies from very small, fractions of an inch,to large statistically homogeneous layers of fifty feet or more.Averaged properties over thicknesses of the order of say one-tenth of awave-length show contrasts with spatial wavelengths from one-tenthwave-length to several wavelengths. Because of spherical spreading andattenuation the ratio of the amplitude of the first arrival refractedwaves, trapped surface waves and direct waves to the deeply reflectedwave amplitues are in the range 80 of 100 db.

The object of seismic surveying is to determine the geometry of thesurface delineating changes in the elastic properties of the rocks sothat the geological structure and structural history can be ascertained.

The advantages of seismic holography over conventional seismic surveysare as follows:

1. The wave arrival time three dimensional volume data of normal seismicsurveying is reduced to a three dimensional display of images of thesource in reflectors and diffracting points.

2. Signal-to-noise is improved since the coherent data are concentratedin space to the images.

3. The images are located in space equivalent to a constant velocitymigration of the reflector space.

Problems which must be solved to make useful seismic holograms are asfollows:

1. No recording medium is available with the necessary dynamic range torecord useful seismic holograms directly as a transparency for opticalreproduction. Hence, means must be provided to reduce the range requiredto preserve the deeper weaker images.

2. The distortions due to irregular surface layers and topography mustbe corrected.

3. Because of the enormous difference between the seismic wavelengths(20 -300 feet) for which the seismic hologram is recorded and theoptical wavelengths (10" feet) with which it is reproduced, largemagnifications of the vertical scale exist in the optical reproduction.

In the elastic half-space for which the seismic hologram is recorded,the reflecting laters are closely spaced and hence the seismic imagesare frequently a fraction to a few wavelengths apart. By using a largereference signal the interference produced by closely spaced coherentimages is essentially eliminated in the hologram. However, the coherentreconstructed images will produce interference fringes. If the verticalexaggeration is large, the fringes will be closely spaced and theoverlapping of the many fringe systems will average to a background towhich will decrease the contrast but not obscure the images. However, ifthe images are close, broader fringes with greater contrast will exist.

BRIEF SUMMARY OF THE INVENTION In a hologram constructed from elasticwaves generated by a continuous source of elastic waves received at aplurality of points on the surface, the ratio of the amplitudes of thesurface and direct waves to the amplitudes of images in deep reflectinglayers can be as large as to db. It is not possible to prepare atransparency for optical reconstruction directly because of the limiteddynamic range of photographic and photochromic materials. The process ofthis invention is to vary the time at which different images radiate bypulsing the source and gating the reception so that very strong and veryweak images are not radiating and being received at the same time. Theduration of the pulse must be sufficiently long that the signalsreceived are substantially coherent. In a preferred embodiment, after asteady state is established, the source is turned off and the hologramis sampled at a plurality of surface locations as a function of the timeelapsed since the source was turned off. Thus at a given time intervalonly those images are radiating that have travel times from source toreceiver location greater than the lapsed time. A programmed gain ineach amplifier is initiated in relation to the turning off of the sourceand the relative location of the receiving seismometer. In a secondembodiment the source is operated for a short interval so that as timeprogresses, images lying within the time interval of the pulse aresequentially illuminated and can thus be recorded at sequential times.

The objective of this invention is to provide a method of reducing thedynamic range required and to improve the signal noise of the seismichologram so that images in deep reflecting surfaces or diffractingdiscontinuities can be reconstructed optically. The objective of thisinvention is accomplished by establishing a steady state with acontinuous coherent source and recording elements of a seismic hologramat a plurality of surface locations as a function of the time after thecontinuous source has been turned off. By using the values of therecorded elements at a selected time, a hologram is obtained for thoseimages which are still radiating at the selected time. Such a hologram,for a time afier the refracted direct and surface waves have died out,will have a dynamic range which makes it possible to construct atransparency suitable for optical reconstruction. To improve the signalto noise ratio, a programmed gain amplifier is actuated at the time thesignal generator is turned off.

In a second embodiment, the coherent source is operated for a short timeinterval so that only a group of images are illuminated at the sametime. As time progresses, successive groups of images at progressivelygreater depths are illuminated. A programmed gain amplifier makes itpossible to record the weak images with a better signal-to-noise ratio.

BRIEF DESCRIPTION OF THE DRAWINGS The invention will be more easilyunderstood from the following detailed description of a preferredembodiment when taken in conjunction with the attached drawings inwhich:

FIG. 1 is a simplified diagram showing a source, two image points, and areceiving location.

FIG. 2 shows schematically the holographic fringe systems produced bythe direct wave and the two image points and their relative amplitudes.

FIG. 3 shows qualitatively the envelope of the hologram as a function ofdistance from the source and time after the source is turned off.

FIG. 4 shows the envelope of the hologram as a function of distance fromthe source and time for a pulse.

FIG. 5 shows schematically circuits to carry out the methods of theinvention.

FIG. 6 shows schematically the effects produced by a programmed gaincontrol.

In FIG. 1 a continuous source of elastic waves 1 is placed at the originof a coordinate system with the xy plane lying on the surface of anelastic half-space. A seismometer 2 at x receives signals from imagepoints 3 and 4. A reference wave voltage corresponding to a plane wavein the xy plane is provided. Let

A be the amplitude of the direct wave and A and A the amplitudes of theimage points. Let A(x,t)be amplitude of the combined sin (wH-Im)sin'wt-l- T3 $72 sin (wt sin (wt-l-Icm) sin (wH-km).

Choose A A A A so that terms not involving A can be neglected. Averagewith respect to time. The resulting hologram is A A X cos Icr For thepurpose of illustration FIG. 2a) shows the variable parts of the fringesystem due to the direct wave, 2b) the fringe system due to image point3 and 2c) the fringe system due to image point 4 for the followingvalues of the parameters:

K 1r/ 1 00, velocity 6060 feet per second z; 2,000 feet, 2;, 20,000feet. The scales show the large range in amplitudes of the order of 10to 1.

In FIG. 3 on the x, t plane the arrival times for signals starting at tO, x are shown. On the vertical axis is shown schematically the envelopeof the hologram and how it changes in time after the source is turnedoff. If the values at a given elapsed time are used as a hologram itsreconstruction would show only those images that were still illuminated.In a practical case, there will be a large number of images and eventhough they will in general not be vertically below the source, it ispreferred to choose values along an arrival time curve.

FIG. 4 shows schematically the envelope of the hologram for a shortwave-train as a function of x or 1. Again a hologram constructed fortimes along an arrival-time curve will, when reconstructed, show onlyimages illuminated during the timewidth of the wave-train.

In these simplified examples a plane horizontal reference wave was usedfor simplicity, but tilted plane or spherical references waves can beused as desired.

FIG. 5 shows a schematic circuit to accomplish the recording of thehologram as a function of the time and with a programmed gain control.Oscillator 5 drives source 7 when switch 6 is closed. After a steadystate has been established the signal at seismometer 8 is constant. Thissignal is amplified by amplifier l0 and mixed with a reference signalfrom oscillator 5 properly phase shifted to correspond with the locationof seismometer 8 in mixer and detector circuit 12. The output isrecorded on the recorder 13 along with signals from other seismometers.If a digital recorder is used, the mixer and detector would include adigitizer. Switch 16 is opened stopping source 7. The absence of voltageacross resistor 14 starts the programmed gain control 9 and themultichannel recorder. FIG. 6 shows schematically how the programmedgain control produces nearly a constant intensity in the hologram.

For pulsed operation switch 6 is closed for a short interval to producea wave-train. The circuits in the gain control and recorder are modifiedto start when a voltage appears across resistor 14. The length of thewave-train must be sufficiently long that it is coherent enough forfringes to exist over the required aperature and yet short enough thatthe large signal from direct waves will have died out before the timesat which a hologram is desired. The frequency spread due to a finitewave-train is approximately inversely proportional to the time width ofthe wave-train. The limiting aperture can be defined as the aperture atwhich the two boundary frequencies have a relative phase difference of1r. If an image is at depth z and observed at x, the variable part of ahologram for wave-length A is cos 2k/A (r-z). Thus for f and fcorresponding to A, and

- z Define angular aperture 04 as twlee tan" 2 where p=number of cyclesin wave-train a tan (1 tan The larger the number of cycles p, thegreater the angle for a given depth. However, if p is large, the directwave will last so long that images for depths less than a critical depthcannot be observed by themselves.

Let t,, be the time for the direct wave to reach x and t be the time fora wave from an image at z to reach 1.

I x, V

t, .x -lzlVwhere V= velocity of the wave. If P is the number of cyclesin the wave-train, the time width of the pulse is p/f where f frequency.For a given 1 the maximum distance x where the arrival from 1 can beobserved after thedirect wave has passed is determined by t 1,, +p/fFrom above the value of a; which satisfies the coherence requirement fora given p is l'lquatiug and squaring both sides 'ihu cubic equation for2 has one real root and two conjugate complex roots. The real root is la J 4 These values of p and x fulfill the conditions that the directwave has passed and that interference fringes exist to the distance xfor a chosen z. These values are important for the shallowest depthimage it is desired to observe. For deeper depths the angular aperturedecreases and no problem arises.

The present invention improves a process for fonning the interferencepattern of a hologram by illuminating an object with a coherent elasticwave, receiving waves that are diffracted and reflected from the objectat a plurality or really dispersed receiving stations with signalsrelating to a reference wave that is appropriately phased. Theimprovement is effected by (a) producing and then terminating theproduction of the coherent elastic wave and (b) mixing the signalsrelating to the reference wave with those relating to the receptions atthe receiving stations at a selected time after the termination of theproduction of the coherent wave at which time waves are being receivedfrom a portion of the illuminated object at a selected relatively longdistance from the receiving stations.

In one embodiment of the present invention, the production of thecoherent wave is tenninated afier a steady state has been establishedand the waves which are received at the receiving locations areamplified by increasing amounts in accordance with a programmed gaincontrol. In another embodiment, starting and stopping of the productionof the coherent wave is timed to produce a relatively short train ofcoherent wave energy and the receptions of waves at the receivingstations is gated to receive waves only during the appearances of wavesthat are returning from a portion of the illuminated object that islocated at a selected relatively long distance from the receivingstations.

I claim as my invention: 1. A process for seismic surveying by producingan acoustic hologram of an underground feature comprising:

illuminating the feature with a steady source of coherent elastic wavesuntil steady state conditions are achieved and then terminating theillumination; receiving at a preselected time after the termination thewaves that are reflected from the feature and converting the receivedwaves to a related electrical signal; mixing the related signal with areference signal corresponding to said coherent elastic waves andrecording the mixed signal; and, utilizing the recorded signal to form aholographic image. 2. A process for seismic surveying by producing anacoustic hologram of an underground feature comprising the steps of:

illuminating the feature with a pulsed source of coherent elastic waves,a given pulse being of sufficient time duration to provide substantialcoherency and terminating at a given time; receiving the waves that arereflected from the feature, beginning at a preselected time after thetermination of the pulse to avoid direct waves, and converting thereceived waves to a related electrical signal; mixing the related signalwith a reference signal corresponding to said coherent elastic waves,and recording the mixed signal; and utilizing the recorded signal toform a holographic image.

1. A process for seismic surveying by producing an acoustic hologram ofan underground feature comprising: illuminating the feature with asteady source of coherent elastic waves until steady state conditionsare achieved and then terminating the illumination; receiving at apreselected time after the termination the waves that are reflected fromthe feature and converting the received waves to a relaTed electricalsignal; mixing the related signal with a reference signal correspondingto said coherent elastic waves and recording the mixed signal; and,utilizing the recorded signal to form a holographic image.
 2. A processfor seismic surveying by producing an acoustic hologram of anunderground feature comprising the steps of: illuminating the featurewith a pulsed source of coherent elastic waves, a given pulse being ofsufficient time duration to provide substantial coherency andterminating at a given time; receiving the waves that are reflected fromthe feature, beginning at a preselected time after the termination ofthe pulse to avoid direct waves, and converting the received waves to arelated electrical signal; mixing the related signal with a referencesignal corresponding to said coherent elastic waves, and recording themixed signal; and utilizing the recorded signal to form a holographicimage.